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首页> 外文期刊>IEEE Transactions on Automatic Control >Compensation of Spatially Varying Input Delay in Distributed Control of Reaction-Diffusion PDEs
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Compensation of Spatially Varying Input Delay in Distributed Control of Reaction-Diffusion PDEs

机译：反应扩散PDE分布式控制中空间变化输入延迟的补偿

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摘要

We develop a predictor-based distributed feedback controller that guarantees exponential stability for a class of reaction-diffusion partial differential equations (PDEs) subject to spatially varying input delay. The delay depends on the location of the input in the spatial domain. In order to design a distributed controller to compensate the spatially varying delay, we first introduce an implicit backstepping transformation, which contains the state of the target system on both sides of the definition and then derive an additional backstepping transformation by a successive integration approach to arrive at a target system that is a distributed cascade of a 2-D transport PDE into a 1-D reaction-diffusion PDE. The resulting delay-compensated controller includes spatially weighted state feedback and feedback of the earlier inputs in four differential spatial regions, which avoids the need for feedback of future inputs, whereas the future input feedback would result if the conventional backstepping transformation was applied. The inverse transformation is also derived, to prove L-2 exponential stability. The applicability and performance of the controller is evaluated in simulation studies.
机译：我们开发了一种基于预测的分布式反馈控制器，其保证了一类反应扩散部分微分方程（PDE）的指数稳定性，其受到空间变化的输入延迟。延迟取决于空间域中输入的位置。为了设计分布式控制器来补偿空间变化的延迟，我们首先引入隐式的反向转换转换，该变换包含定义的两侧上的目标系统状态，然后通过连续的集成方法来实现额外的反向转换转换在一个目标系统，其是将2-D传输PDE的分布式级联进入1-D反应扩散PDE。所得到的延迟补偿控制器包括空间加权状态反馈和四个差分空间区域中的前面输入的反馈，其避免了对未来输入反馈的需要，而如果应用了传统的反向转换，则将导致未来的输入反馈。还导出逆变换，以证明L-2指数稳定性。在仿真研究中评估了控制器的适用性和性能。

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